Math: How to Multiply Two Binomials (FOIL) Practice
Practice using First, Outer, Inner, Last to expand binomial products
Math: How to Multiply Two Binomials (FOIL) Practice
Practice using First, Outer, Inner, Last to expand binomial products
Math - Grade 6-8
- 1
Multiply and simplify: (x + 3)(x + 5).
Use First, Outer, Inner, Last, then combine the x terms.
The product is x^2 + 8x + 15 because x times x is x^2, the outer and inner terms make 5x + 3x = 8x, and 3 times 5 is 15. - 2
Multiply and simplify: (x + 2)(x + 7).
The product is x^2 + 9x + 14 because the middle terms are 7x and 2x, which combine to 9x. - 3
Multiply and simplify: (y + 4)(y - 6).
Pay close attention to the negative sign in y - 6.
The product is y^2 - 2y - 24 because the outer and inner terms are -6y and 4y, which combine to -2y. - 4
Multiply and simplify: (a - 3)(a - 8).
The product is a^2 - 11a + 24 because the outer and inner terms are -8a and -3a, and the last terms multiply to positive 24. - 5
Multiply and simplify: (2x + 1)(x + 4).
Remember that 1 times x is x.
The product is 2x^2 + 9x + 4 because 2x times x is 2x^2, the middle terms are 8x and 1x, and 1 times 4 is 4. - 6
Multiply and simplify: (3m + 2)(m + 5).
The product is 3m^2 + 17m + 10 because the outer and inner terms are 15m and 2m, which combine to 17m. - 7
Multiply and simplify: (2p - 5)(p + 3).
A positive term and a negative term can partly cancel when you combine like terms.
The product is 2p^2 + p - 15 because the outer and inner terms are 6p and -5p, which combine to p. - 8
Multiply and simplify: (4x - 1)(x - 2).
The product is 4x^2 - 9x + 2 because the outer and inner terms are -8x and -1x, and -1 times -2 is positive 2. - 9
Multiply and simplify: (n + 9)(n - 9).
This is a difference of squares pattern: (a + b)(a - b) = a^2 - b^2.
The product is n^2 - 81 because the outer and inner terms are -9n and 9n, which cancel to 0. - 10
Multiply and simplify: (5r + 6)(2r - 3).
The product is 10r^2 - 3r - 18 because the middle terms are -15r and 12r, which combine to -3r. - 11
A rectangle has side lengths (x + 6) units and (x + 4) units. Write an expression for the area of the rectangle in simplified form.
Area of a rectangle equals length times width.
The area is x^2 + 10x + 24 square units because area is length times width, so (x + 6)(x + 4) expands to x^2 + 10x + 24. - 12
A student says that (x + 4)(x + 3) equals x^2 + 12 because they multiplied only the first terms and the last terms. Explain the mistake and give the correct product.
FOIL has four products, not just two.
The mistake is that the student forgot the outer and inner products. The correct product is x^2 + 7x + 12 because the missing terms are 3x and 4x, which combine to 7x.