Multiply the polynomials (4x^2+4x+6)(7x+5)

28x^3 +48x^2 +62x +30

Step-by-step explanation:

You can use the distributive property to identify the separate terms, then combine terms:

... = 7x(4x^2 +4x +6) +5(4x^2 +4x +6)

... = 28x^3 +28x^2 +42x + 20x^2 +20x +30

... = 28x^3 +x^2(28+20) +x(42 +20) +30

... = 28x^3 +48x^2 +62x +30

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Or, you can recognize where the product terms come from, and combine terms as you go. This can be done in your head as you write down the answer.

... The x^3 term comes from 7x·4x^2 = 28x^3

... The x^2 term comse from 7x·4x +5·4x^2 = 28x^2 +20x^2 = 48x^2

... The x term comes from 7x·6 +5·4x = 42x +20x = 62x

... The constant term comes from 5·6 = 30

So, you can write down the result as 28x^3 +48x^2 +62x +30.