Question

expand the following (3x-4y-5)^2​

Answer 1

Answer: They are expanded as follows.

Step-by-step explanation:

Concept: A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It is made up of indeterminates (also known as variables) and coefficients.

x2-4x + 7 is an illustration of a polynomial with a single indeterminate x.

Now here we are given 2 polynomials raised to the power 2 and we are asked to expand them.

So we proceed as follows using the formula (a + b + c)^2 = a^2 + b^2 + c^2 +2ab+2bc +2ca:

$(3x-4y-5)^{2} \\= (3x)^{2} +(-4y)^{2} +(-5)^{2} +2*3x*(-4y)+2*(-4y)*(-5)+2*(-5)*(3x)\\=9x^{2} +16y^{2} +25-24xy+40y-30x$

$(-2x+6y+4)^{2} \\= (-2x)^{2} +(6y)^{2} +(4)^{2} +2*(-2x)*6y+2*6y*4+2*(-2x)*4\\=4x^{2} +36y^{2} +16-24xy+48y-16x$

Final Ans: $(3x-4y-5)^{2}$ is expanded as $9x^{2} +16y^{2} +25-24xy+40y-30x$ and $(-2x+6y+4)^{2}$ is expanded as $4x^{2} +36y^{2} +16-24xy+48y-16x$.