Question

simplify: 2/7(14x²-21y²)(-5x²-3y²)

Answer 1

GIVEN :

Simplify : $\frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)$

TO FIND :

The simplified terms of the given expression $\frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)$

SOLUTION :

Given expression is $\frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)$

Now solving the given expression as below :

$\frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)$

$=\frac{2}{7}(7(2x^2-3y^2))(-5x^2-3y^2)$

$=2(2x^2-3y^2)(-5x^2-3y^2)$

$=2(2x^2)-2(3y^2)(-5x^2-3y^2)$

By using the Distributive property :

a(x-y)=ax-ay

$=(4x^2-6y^2)(-5x^2-3y^2)$

$=4x^2(-5x^2-3y^2)-6y^2(-5x^2-3y^2)$

By using the Distributive property :

(a+b)(x+y)=(a+b)x+(a+b)y

$=4x^2(-5x^2)+4x^2(-3y^2)-6y^2(-5x^2)-6y^2(-3y^2)$

By using the Distributive properties :

i) a(x+y)=ax+ay

ii) a(x-y)=ax-ay

By using the exponent property :

$a^m.a^n=a^{m+n}$

$=-20x^4-12x^2y^2+30x^2y^2+18y^4$

$=-20x^4+18x^2y^2+18y^4$

$\frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)=-20x^4+18x^2y^2+18y^4$

∴ the simplified terms for the given expression $\frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)$ is $-20x^4+18x^2y^2+18y^4$