Question

Factorise 12a^b+15ab^2​

Answer 1

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$\huge{\underline{\sf{\red{Required\:Answer:}}}}$

$:\implies\:\:\sf{12a^2b=2\times2\times3\times a \times a\times b}$

$:\implies\:\:\sf{15ab^2=3\times5\times a\times b \times b }$

Now,

$:\implies\:\:\sf{12a^2b+15ab^2}$

$:\implies\:\: \sf {3(3 \times a \times b\times2\times2\times a)+(3\times a\times \times b \times 5 \times b )}$

$:\implies\:\: \sf {3 \times a \times b[(2\times2\times a)+( 5 \times b )]}$

$:\implies\:\: \sf {3 a b\times(4a+5b)}$

$:\implies\:\: \sf {3 a b(4a+5b)}$

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$\huge{\underline{\sf{\orange{Required\:Answer:}}}}$

$:\implies\: \sf{10x^2=2 \times 5 \times x \times x}$

$:\implies\:\sf{18x^3=2 \times 3 \times 3 \times x\times x\times x}$

$:\implies\: \sf{14x^4=2 \times 7 \times x \times x\times x\times x}$

Now,

$:\implies\: \sf{10x^2-18x^3+14x^4}$

$:\implies\:\sf{(2 \times x \times x \times 5)-(2 \times x \times x \times 3 \times 3 \times x)}$

$:\implies\:\sf{+ (2\times x \times x \times 7 \times x\times x)}$

$:\implies\:\: \sf{2\times x \times x \times [(5-(3 \times 3 \times x) +(7\times x \times x)] }$

$:\implies\:\: \sf{2x^2 \times (5-9x+7x^2) }$

$:\implies\:\: \sf{2x^2(7x^2-9x +5)}$

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Answer 2

12a²b+15ab²

=3ab(4a+5b)