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Expand the expression
Answer
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Factorize the expression
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$2 \left( p+q \right) ^{ 2 } - \left( p+q \right) p-6p ^{ 2 }$
$- 5 p ^ { 2 } + 3 p q + 2 q ^ { 2 }$
Organize polynomials
$2 \left ( \color{#FF6800}{ p } \color{#FF6800}{ + } \color{#FF6800}{ q } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( p + q \right ) p - 6 p ^ { 2 }$
$ $ Expand the binomial expression $ $
$2 \left ( \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } \right ) - \left ( p + q \right ) p - 6 p ^ { 2 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } \right ) - \left ( p + q \right ) p - 6 p ^ { 2 }$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 4 } \color{#FF6800}{ p } \color{#FF6800}{ q } + \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } - \left ( p + q \right ) p - 6 p ^ { 2 }$
$2 p ^ { 2 } + 4 p q + 2 q ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ p } \color{#FF6800}{ + } \color{#FF6800}{ q } \right ) p - 6 p ^ { 2 }$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$2 p ^ { 2 } + 4 p q + 2 q ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ p } \color{#FF6800}{ - } \color{#FF6800}{ q } \right ) p - 6 p ^ { 2 }$
$2 p ^ { 2 } + 4 p q + 2 q ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ p } \color{#FF6800}{ - } \color{#FF6800}{ q } \right ) \color{#FF6800}{ p } - 6 p ^ { 2 }$
$ $ Organize the expression with the distributive law $ $
$2 p ^ { 2 } + 4 p q + 2 q ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ p } \color{#FF6800}{ q } - 6 p ^ { 2 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } }$
$ $ Organize the similar terms $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } + \left ( 4 - 1 \right ) p q + 2 q ^ { 2 }$
$ $ Arrange the constant term $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } + \left ( 4 - 1 \right ) p q + 2 q ^ { 2 }$
$- 5 p ^ { 2 } + \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ p } \color{#FF6800}{ q } + 2 q ^ { 2 }$
$ $ Arrange the constant term $ $
$- 5 p ^ { 2 } + \color{#FF6800}{ 3 } \color{#FF6800}{ p } \color{#FF6800}{ q } + 2 q ^ { 2 }$
$- \left ( 5 p ^ { 2 } - 3 p q - 2 q ^ { 2 } \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ p } \color{#FF6800}{ + } \color{#FF6800}{ q } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ p } \color{#FF6800}{ + } \color{#FF6800}{ q } \right ) \color{#FF6800}{ p } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } }$
$ $ Expand the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } }$
$ $ Bind the expressions with the common factor $ - 1$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } \right )$
Solution search results
search-thumbnail-If the sum of two consecutive numbers is $45$ and one number is $X$ .This statement in the form of equation $1s:$ $\left(1$ Point) $\right)$ $○5x+1$ $1eft\left(x+1$ $r1gnt\right)=45s$ $○sx+1ef\left(x+2$ $r1gnt\right)=145s$ $sx+1x=45s$
7th-9th grade
Algebra
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search-thumbnail-$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ $s1S$ $S-1S$ $s2S$ $s50s$
7th-9th grade
Other
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search-thumbnail-The is the statement of the Mean Value Theorem from your $te\times tb00k$ $Tneoren$ $m4.5$ $Ne8n$ Value Theorem Let f be continuous over $leclose$ interval $\left(a.b\right)aod$ $i$ $eo$ $xd$ $csnlc$ $\left(ab\right)$ $mmd$ exists at least one point cE $\left(a.b\right)$ $si1dhtba$ $f^{'}\left(c\right)=\dfrac {f\left(b\right)-f\left(a\right)} {b-a}$ What is the geometric interpretation of the conclusion of the theorem? O The tangent line to the graph of \(f\left(x\right)\) at $l\left(c1\right)$ is parallel to the secant line connecting \(\left(a,f\left(a\right)\right)\) and \(\left(b,f\left(b\right)\right)\). O The tangent line to the graph of $\left(f\left(lef\left(x\left(right\right)$ at \(c\) is the secant line connecting \(\left(a,f\left(a\right)\right)\) $ana$ \(\left(b,f\left(b\right)\right)\). O The tangent line to the graph $of$ $\left(f\left(leF\left(x\left(right\right)\left(\right)at1\left(c1\right)is$ perpendicular to the secant line connecting \(\left(a,f\left(a\right)\right)\) and A(\left(b,f\left(b\right)\right)\). O The tangent line to the graph of $\left(fleH\left(x\right)nght\right)\right)\right)$ $at$ $\left(c\right)\right)ishoizonta|$ $Tnere$ is more than one tangent line to the graph $0no$ $\left(flcf\left(x\right)night\right)\left($ $at1\left(c1\right)$
Calculus
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search-thumbnail-What is the inverse of $g\left(x\right)=\sqrt{x-1} $ $Og\left(x\right)=\sqrt{x+1} $ $+1$ $g^{'}\left(x\right)=5-$ $y_{9}$ $g\sqrt{ef\left(x\left(nght\right)} =\left(f_{tac\left(x+1\right)0sq\pi \left(x\right)}$ $Og^{'}\left(x\right)=x^{2}+1$ $○g\left(x\right)=x^{2}-1$ « Previous Ne
Other
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search-thumbnail-What is the inverse of $g\left(x\right)=\sqrt{x-1} $ $Og\left(x\right)=\sqrt{x+1} $ $+1$ $g^{'}\left(x\right)=5-$ $y_{9}$ $g\sqrt{ef\left(x\left(nght\right)} =\left(f_{tac\left(x+1\right)0sq\pi \left(x\right)}$ $Og^{'}\left(x\right)=x^{2}+1$ $○g\left(x\right)=x^{2}-1$ « Previous Ne
Other
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