Question

1. (x + y + 4)^2

2. (4x + y)^2

3. (8p + q - r)^3

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Answer 1

Answer:

1) (x + y + 4)²

=x²+y²+4²+2.x.y+2.y.4+2.4.x. [From the rule:(a+b+c)²=a²+b²+c²+2ab+2bc+2ca]

=x²+y²+16+2xy+8y+8x

2) (4x + y)²

=(4x)²+2.4x.y+y²

=16x²+8xy+y² [From the rule:(a+b)²=a²+b²+2ab]

3) (8p + q - r)³

=(8p + q - r)² × (8p + q - r)

=[(8p)²+q²+r²+2.8p.q - 2.q.r - 2.8p.r] × (8p + q - r)

[From the rule (a+b-c)²= a²+b²+c²+2ab-2bc-2ca

=[64p²+q²+r²+16pq-2qr-16pr] × (8p + q - r)

=8p[64p²+q²+r²+16pq-2qr-16pr]+ q[64p²+q²+r²+16pq-2qr-16pr] - r [64p²+q²+r²+16pq-2qr-16pr]. =512q³+8pq²+8pr²+128p²q-16pqr-128p²r+ 64p²q+ +q³+qr²+16pq²-2q²r-16pqr-64p²r - q²r-r³-16pqr + 2qr²+16pr²

=[512p³+24pq²+24pr²+192 p²q-48pqr- 192p²r-3q²r+3qr²+q³-r³ (Ans)