Question

Rewrite each expression as a sum or difference of terms. (i) (x+3)(x-3) (ii) (x^2-3)(x^2+3) (iii) (x^15+3)(x^15-3) (iv) (x-3)(x^2-9)(x+3) (v) (x^2+y^2)(x^2-y^2) (vi) (x^2+y^2)^2 (vii) (x-y)²(x+y)²
(viii) (x-y)²(x²+y²)² (x+y)²

Answer 1

Answer:

All the answers are given below.

Step-by-step explanation:

(i) (x+3)(x-3) =x² -3² =x² -9 {Since (a+b)(a-b) =a² -b²}

(ii) (x²-3)(x²+3) =(x²)² -3² =$x^{4} -9$ {Since (a+b)(a-b) =a² -b²}

(iii) $(x^{15} +3)(x^{15}-3) =(x^{15} )^{2}-3^{2} =x^{30} -9$

(iv) (x-3)(x²-9)(x+3) =(x²-9)(x²-9)=(x²-9)²=$x^{4}-18x^{2} +81${Since, (a-b)² =a²-2ab+b²}

(v) (x²+y²)(x²-y²) = (x²)² -(y²)² =$x^{4}-y^{4}$

(vi) (x²+y²)² =$x^{4}+2x^{2} y^{2} +y^{4}$ {Since (a+b)² =a²+2ab+b²}

(vii) (x-y)²(x+y)² =(x²-y²)² =$x^{4} -2x^{2} y^{2}+y^{4}$ {Since (a-b)² =a²-2ab+b² and (a+b)(a-b) =a²-b²}

(viii) (x-y)²(x²+y²)²(x+y)² =(x²+y²)²(x²-y²)² =$(x^{4} -y^{4} )^{2} =x^{8}-2x^{4} y^{4} +y^{8}$ (Answer)