Question

(4х+7)^2 (а^4-2b^2)^2

Answer 1

Ответ: если их нужно упростить, то вот:

1.(4х+7)^2= 16x^2+56x+49.

2. (a^4-2b^2)^2=a^8-4a^4b^2+4b^4.

Answer 2

To expand the expression $(4x + 7)^2 (a^4 - 2b^2)^2$, you can use the distributive property of multiplication to expand each term within the parentheses and then multiply the results. Here's the step-by-step expansion:

1. Expand $(4x + 7)^2$:

   $(4x + 7)^2 = (4x + 7)(4x + 7)$

   Use the FOIL method (First, Outer, Inner, Last) to expand this expression:

   $(4x + 7)(4x + 7) = (4x * 4x) + (4x * 7) + (7 * 4x) + (7 * 7)$

   Simplify each term:

   $(16x^2) + (28x) + (28x) + (49)$

   Combine like terms:

   $(16x^2) + (56x) + (49)$

2. Expand $(a^4 - 2b^2)^2$:

   $(a^4 - 2b^2)^2 = (a^4 - 2b^2)(a^4 - 2b^2)$

   Use the FOIL method again to expand this expression:

   $(a^4 - 2b^2)(a^4 - 2b^2) = (a^4 * a^4) - (2b^2 * a^4) - (a^4 * 2b^2) + (4b^4)$

   Simplify each term:

   $(a^8) - (2a^4b^2) - (2a^4b^2) + (4b^4)$

   Combine like terms:

   $(a^8) - (4a^4b^2) + (4b^4)$

3. Now, multiply the two expanded expressions together:

   $(16x^2 + 56x + 49)(a^8 - 4a^4b^2 + 4b^4)$

4. Use the distributive property to multiply each term in the first expression by each term in the second expression:

   $(16x^2)(a^8) + (16x^2)(-4a^4b^2) + (16x^2)(4b^4) + (56x)(a^8) + (56x)(-4a^4b^2) + (56x)(4b^4) + (49)(a^8) + (49)(-4a^4b^2) + (49)(4b^4)$

5. Simplify each term:

   $16x^2a^8 - 64x^2a^4b^2 + 64x^2b^4 + 56xa^8 - 224xa^4b^2 + 224xb^4 + 49a^8 - 196a^4b^2 + 196b^4$

So, the fully expanded expression is:

$16x^2{a}^8-64x^2{a}^4{b}^2+64x^2{b}^4+56x{a}^8-224x{a}^4{b}^2+224x{b}^4$