Simplify: 2/7(14x²-21y²)(-5x²-3y²)

1.	Simplify: 2/7(14x²-21y²)(-5x²-3y²)
Answer» 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 $-20x^4+18x^2y^2+18y^4$

Answer»

GIVEN :

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