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Formula
Factorize the expression
Answer
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$a ^{ 4 } -a ^{ 2 } -56$
$\left ( a ^ { 2 } - 8 \right ) \left ( a ^ { 2 } + 7 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 56 }$
$ $ Use the factoring formula, $ x^{2} + \left(a+b\right)x + ab = \left(x+a\right)\left(x+b\right)$
$\left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right )$
$\left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \right )$
Solution search results
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(v) () (-x) (x") (– x2) (vi) 0.9p q (10p- 20g) 
(vi) (7x- $-11x+10\right)\left(x^{3}-x^{2}$ $\left(\dfrac {10} {9}a^{5}b^{6}c^{6}\right)\left(-\dfrac {3} {2}b^{2}c\right)\left(\dfrac {6} {5}c^{3}α^{4}\right)\left(-a^{3}d$ 
(ix) $\left(0.7x^{3}-0.5y^{3}\right)\left(0.7x^{3}+0.5y^{3}\right)$ (x) $\left(64a^{2}-56ab+49b^{2}\right)$ (8a + 7b) 
3. Find the variable part in the product of: 
y, 255xyp and 313y z 167 1 $\dfrac {97} {43}b^{3},\dfrac {29} {41}a^{6}band\dfrac {111} {123}$ 
0 127x 

4. Express $\left(5x^{5}$ $\right)\left(12x^{2}y\right)\left(\dfrac {3} {20}xy^{2}\right)$ as a monomial and then evaluate it for x = 1, y = 2. 
5. Express 1.5a (10ab-4b²) as a binomial and then evaluate it for a = - 2, b = 3. 
6. Simplify and then verify the result for the given values. 
) $\left(3x-4y\right)\left(4x^{2}y+3xy^{2}\right):x=2,y=-1$ 
(11) $\left(\dfrac {1} {4}a^{2}+\dfrac {5} {9}b^{2}\right)\left(a+b+ab\right)$ ; a = 2, b= 3 
(1i) $\left(x^{3}y-y^{2}\right)\left(x^{3}y+y^{2}\right):x=-1,y=-2$ 
(iv) $\left(2p+3q\right)\left(4p^{2}+12pq+9q^{2}\right):p=\dfrac {1} {2},9=\dfrac {1} {3}$ 
$\left(\right)$ $\left(m^{2}+mn+m^{2}$ $\right)\left(m-n\right):m=4,n=3$ 
7. Simplify: 
) $3x^{2}\left(3y^{2}+2\right)-x\left(x-2xy^{2}\right)+y\left(2x^{2}y-2y$ 
(1) $\left(2x+7\right)\left(5x+9\right)-\left(4x^{2}+1\right)\left(x-3\right)$ 
(ii) $\left(y^{2}-7y+4\right)\left(3y^{2}-2\right)+\left(y+1\right)\left(y^{2}+2y$
7th-9th grade
Algebra
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25. $a^{2}-ay-210y^{2}$ 
$28.$ $x^{2}+16x-260$ 29 
$31$ $a^{4}-a^{2}b^{2}-56b^{4}$ 32 
34. $a^{2}b^{2}-3abc-10c^{2}$ 
$-243x^{2}y^{2}$ 
$36.$ $a^{2}-18axy-$ 
$38$ $x^{4}-a^{2}x^{2}-132a^{4}$ 
$40.$ $x^{6}+x^{3}-870$ 
43. $110-x-x^{2}$ x2. 
$46$ $65+8xy-x^{2}y^{2}$
1st-6th grade
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