Find the product of the following binomials: (5 − 2x)(3 + x), (−x + 7y)(7x − y), (a2 + b)(a + b2), and (p2…

Question

Find the product of the following binomials: (5 − 2x)(3 + x), (−x + 7y)(7x − y), (a2 + b)(a + b2), and (p2 - q2)(2p + q).

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the 2nd question:

2. Find the product.

Use the distributive property (FOIL method).
$$ (5 - 2x)(3 + x) = 5(3) + 5(x) - 2x(3) - 2x(x) $$
Perform the multiplications.
$$ = 15 + 5x - 6x - 2x^2 $$
Combine like terms.
$$ = \boxed{15 - x - 2x^2} $$
- 2 (ii): $(-x + 7y)(7x - y)$
Use the distributive property (FOIL method).
$$ (-x + 7y)(7x - y) = -x(7x) - x(-y) + 7y(7x) + 7y(-y) $$
Perform the multiplications.
$$ = -7x^2 + xy + 49xy - 7y^2 $$
Combine like terms.
$$ = \boxed{-7x^2 + 50xy - 7y^2} $$
- 2 (iii): $(a^2 + b)(a + b^2)$

$$
(a^2 + b)(a + b^2) = a^2(a) + a^2(b^2) + b(a) + b(b^2)
$$

Perform the multiplications.
$$ = \boxed{a^3 + a^2b^2 + ab + b^3} $$
- 2 (iv): $(p^2 - q^2)(2p + q)$

$$
(p^2 - q^2)(2p + q) = p^2(2p) + p^2(q) - q^2(2p) - q^2(q)
$$

Find the product of the following binomials: (5 - 2x)(3 + x), (-x + 7y)(7x - y), (a2 + b)(a + b2), and (p2 - q2)(2p + q).