(A) To expand the expression $(4a - b + 2c)^2$,we use the algebraic identity:$(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx$Here,$x = 4a$,$y = -b$

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$16a^2 + b^2 + 4c^2 - 8ab - 4bc + 16ac$

(A) To expand the expression $(4a - b + 2c)^2$,we use the algebraic identity:$(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx$Here,$x = 4a$,$y = -b$,and $z = 2c$.Substituting these values into the identity:$(4a - b + 2c)^2 = (4a)^2 + (-b)^2 + (2c)^2 + 2(4a)(-b) + 2(-b)(2c) + 2(2c)(4a)$Calculating each term:$= 16a^2 + b^2 + 4c^2 - 8ab - 4bc + 16ac$

Class 9 Mathematics Polynomials Mix Examples - Polynomials

Medium

Expand the following:
$(4a - b + 2c)^2$

A
$16a^2 + b^2 + 4c^2 - 8ab - 4bc + 16ac$
B
$16a^2 + b^2 + 4c^2 + 8ab - 4bc + 16ac$
C
$16a^2 + b^2 + 4c^2 - 8ab + 4bc + 16ac$
D
$16a^2 + b^2 + 4c^2 - 8ab - 4bc - 16ac$

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Expand the following:$(4a - b + 2c)^2$

Similar Questions

Find $p(1)$,$p(2)$,and $p(4)$ for the following polynomial: $p(t) = t^{2} - 6t + 8$.

Factorise the following quadratic polynomial by splitting the middle term:$x^{2}-4x-77$

From the following polynomials,find out which of them has $(x+1)$ as a factor:$P(x) = 6x^3 + 11x^2 - 5x - 12$

From the following polynomials,find out which of them has $(x-1)$ as a factor:$x^{3}+6x^{2}-9x-14$

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = 4x^3 - 12x^2 + 14x - 3$ and $g(x) = 2x - 1$.

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Expand the following:
$(4a - b + 2c)^2$

Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}-4x-77$

From the following polynomials,find out which of them has $(x+1)$ as a factor:
$P(x) = 6x^3 + 11x^2 - 5x - 12$

From the following polynomials,find out which of them has $(x-1)$ as a factor:
$x^{3}+6x^{2}-9x-14$