Question

(3a-4b+2c)^2 expand the following using suitable identities
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Answer 1

The expansion of (3a - 4b + 2c)²  is $9a^{2}+16b^{2}+4c^{2}-24ab-16bc+12ca$.

Step-by-step explanation:

The expansion of (a + b + c)² is:

(a + b + c)² = a² + b² + c + 2 (ab + bc + ca)

The expression is:

(3a - 4b + 2c)²

Expand the expression provided using the identity mentioned above as follows:

$(3a - 4b + 2c)^{2}\\=(3a)^{2}+(-4b)^{2}+(2c)^{2}+2[(3a\times -4b)+(-4b\times 2c)+(2c\times 3a)]\\=9a^{2}+16b^{2}+4c^{2}+2(-12ab-8bc+6ca)\\=9a^{2}+16b^{2}+4c^{2}-24ab-16bc+12ca$

Thus, the expansion of (3a - 4b + 2c)²  is $9a^{2}+16b^{2}+4c^{2}-24ab-16bc+12ca$.

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Answer 2

(3a-4b+2c)^2

=(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca

=(3a)^2+(-4b)^2+(2c)^2+2(3a)(-4b)+2(-4b)(2c)+2(2c)(3a)

=9a^2-16b^2+4c^2-24ab-16bc+12ca

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Step-by-step explanation: