Factor: -36x^{7}y^{3} - 63x^{4}y^{5}

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Hi Jesi ka,

First, let P = the polynomial you show above.

Then, try rewriting the two terms of P so that the powers that appear in each look more alike:

P = -3 * 12 * x^3 * x*4 * y^3 - 3 * 21 * x^4 * y^3 * y^2 (using the addition rule for exponents)

Now factor out the things that are common to the first and second term:

P = 3 * x^4 * y^3 * [ -12 * x^3 - 21 * y^2]

But, notice that -12 and -21 have a common factor of -3: that is, -12 = -3 * 4 and -21 = -3 *7, so

P = -3 * 3 * x^4 * y^3 * [ 4 * x^3 + 7 * y^2] = -9x^4y^3 [4x^3 + 7y^2]

CHECK:

Using the distributive law of multiplication, we get

-9x^4y^3 [4x^3 + 7y^2] = -9x^4y^3 [4x^3] + -9x^4y^3 [7y^2] = -36x^7y^3 -63x^4y^5

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