Question

Expand each ofthe following, using suitable identities:
(i)(x+2y+4z)²
(ii)(2x-y+z)²
(iii)(3a-7b+c)²
(iv)(-2x-y-3z)²

Answer 1

Answer:

$(i)x^{2}+4y^{2}+16z^{2}+4xy+16yz+8zx$

$(ii)4x^{2}+y^{2}+z^{2}-4xy-2yz+4zx$

$(iii)9a^{2}+49b^{2}+c^{2}-42ab-14bc+6ac$

$(iv)4x^{2}+y^{2}+9z^{2}+4xy+6yz+12zx$

Step-by-step explanation:

$\textrm{using thr identity (p+q+r)^{2}=p^{2}+q^{2}+r^{2}+2pq+2qr+2rp}$

$(x+2y+4z)^{2}=x^{2}+4y^{2}+16z^{2]+4xy+16yz+8zx$

$(2x-y+z)^{2}=4x^{2}+y^{2}+z^{2}-4xy-2yz+4zx$

$(3a-7b+c)^{2}=9a^{2}+49b^{2}+c^{2}-42ab-14bc+6ac$

$(-2-y-3z)^{2}=4x^{2}+y^{2}+9z^{2}+4xy+6yz+12zx$

Answer 2

Answer:

x² +  4y² + 16z² + 4xy + 8xz + 16yz

4x² + y²  + z² - 4xy + 4xz - 2yz

9a² + 49b²+ c² - 42ab  + 6ac - 14bc

4x² + y²+ 9z² + 4xy + 12xz + 6yz

Step-by-step explanation:

(x+2y+4z)²

using (a + b)² = a² + b² + 2ab

a = x + 2y  & b = 4z

= (x + 2y)² + (4z)² +2(x + 2y)4z

= x² + 4y² + 4xy + 16z² + 8xz + 16yz

= x² +  4y² + 16z² + 4xy + 8xz + 16yz

(2x-y+z)²

= (2x- y)² + z² + 2(2x - y)z

using (a - b)² = a² + b² - 2ab

= 4x² + y² - 4xy + z² + 4xz - 2yz

= 4x² + y²  + z² - 4xy + 4xz - 2yz

(3a-7b+c)²

= (3a - 7b)² + c²  + 2(3a - 7b)c

= 9a² + 49b² - 42ab + c² + 6ac - 14bc

= 9a² + 49b²+ c² - 42ab  + 6ac - 14bc

(-2x-y-3z)²

= (-1)²(2x + y + 3z)²

= (2x + y + 3z)²

= (2x + y)² + (3z)² + 2(2x +y)3z

= 4x² + y² + 4xy + 9z² + 12xz + 6yz

= 4x² + y²+ 9z² + 4xy + 12xz + 6yz